giải pt :3√x-1 + √9x-9 – √25x-25 + 2√4x-4 =24

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1. Đáp án:

   $x = \dfrac{601}{25}$

   Giải thích các bước giải:

   $3\sqrt{x – 1} + \sqrt{9x -9} – \sqrt{25x – 5} + 2\sqrt{4x – 4} = 24$ $(*)$

   $ĐK:\, x \geq 1$

   $(*) 3\sqrt{x – 1} + \sqrt{9(x -1)} – \sqrt{25(x – 1)} + 2\sqrt{4(x – 1)} = 24$

   $\Leftrightarrow 3\sqrt{x – 1} + 3\sqrt{x – 1} – 5\sqrt{x – 1} + 4\sqrt{x – 1} = 24$

   $\Leftrightarrow 5\sqrt{x – 1} = 24$

   $\Leftrightarrow \sqrt{x – 1} = \dfrac{24}{5}$

   $\Rightarrow x – 1 = \dfrac{576}{25}$

   $\Rightarrow x = \dfrac{601}{25}$ (nhận)

   Vậy $x = \dfrac{601}{25}$

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2. `3sqrt{x – 1} + sqrt{9x – 9} – sqrt{25x – 25} + 2sqrt{4x – 4} = 24` `(ĐK: x >= 1)`

   `<=> 3sqrt{x – 1} + 3sqrt{x – 1} – 5sqrt{x – 1} + 4sqrt{x – 1} = 24`

   `<=> 5sqrt{x – 1} = 24`

   `<=> sqrt{x – 1} = 24/5`

   `<=> x – 1 = 576/25`

   `<=> x = 601/25`

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